Finite Group Databasebeta

← C22×#10623181 #15660763

Subgroups — C22×#10623181 #15660763

Order 2816.

7934 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623181C2148yesmaximal, direct product factor
2C22×#66932C211yesmaximal, characteristic, complemented
3C22×#66932C211yesmaximal, characteristic, complemented
4C22×#66943C211yesmaximal, characteristic, complemented
5C22×#66942C211yesmaximal, characteristic, complemented
6C22×#66942C211yesmaximal, characteristic, complemented
7C22×#66988C211yesmaximal, characteristic
8C22×#66931C211yesmaximal, characteristic, complemented
9C22×#66931C211yesmaximal, characteristic, complemented
10C22×#66940C211yesmaximal, characteristic, complemented
11C22×D4×Dic11C211yesmaximal, characteristic
12C22×#66979C211yesmaximal, characteristic, complemented
13C22×#66930C211yesmaximal, characteristic, complemented
14C22×#66930C211yesmaximal, characteristic, complemented
15C23×Dic11⋊C4C211yesmaximal, characteristic, complemented
16C22×C11×#123C211yesmaximal, characteristic
17C23×D4×C11C2211yescharacteristic
18C24×C4×C11C2211yescharacteristic
19C24×Dic11C2211yescharacteristic
20C24×Dic11C2211yescharacteristic
21C24×Dic11C2211yescharacteristic
22C23×Dic22C2211yescharacteristic
23C2×C11×#123C22124yes—
24C22×C11×C4⋊C4C2211yescharacteristic
25C22×C11×C4⋊C4C2211yescharacteristic
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C22×C22⋊Dic11C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C22×C22⋊Dic11C2211yescharacteristic
33C22×C22⋊Dic11C2211yescharacteristic
34C2×#66988C22124yes—
35C2×D4×Dic11C22124yes—
36C2×#66979C22124yescomplemented
37C22×C4⋊Dic11C2211yescharacteristic
38C22×C4⋊Dic11C2211yescharacteristic
39C22×C4⋊Dic11C2211yescharacteristic
40C22×C4⋊Dic11C2211yescharacteristic
41C22×Dic11⋊C4C2211yescharacteristic
42C22×Dic11⋊C4C2211yescharacteristic
43C22×Dic11⋊C4C2211yescharacteristic
44C22×Dic11⋊C4C2211yescharacteristic
45C22×Dic11⋊C4C2211yescharacteristic
46C22×Dic11⋊C4C2211yescharacteristic
47C22×Dic11⋊C4C2211yescharacteristic
48C22×Dic11⋊C4C2211yescharacteristic
49C22×Dic11⋊C4C2211yescharacteristic
50C22×Dic11⋊C4C2211yescharacteristic
51C22×Dic11⋊C4C22124yescomplemented
52C22×C4×Dic11C2211yescharacteristic
53C22×C4×Dic11C2211yescharacteristic
54C22×C4×Dic11C2211yescharacteristic
55C22×C4×Dic11C2211yescharacteristic
56C22×C4×Dic11C2211yescharacteristic
57#10623181C221256yesdirect product factor
58C2×#66943C22124yescomplemented
59C2×#66942C22124yescomplemented
60C2×#66942C22124yescomplemented
61C2×#66940C22124yescomplemented
62C2×#66932C22124yescomplemented
63C2×#66932C22124yescomplemented
64C2×#66931C22124yescomplemented
65C2×#66931C22124yescomplemented
66C2×#66930C22124yescomplemented
67C2×#66930C22124yescomplemented
68C25×C11C2311yescharacteristic
69C25×C11C2311yescharacteristic
70C22×D4×C11—28no—
71C22×D4×C11C23112yes—
72C23×C4×C11—28no—
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C23112yes—
79C23×Dic11—28no—
80C23×Dic11—28no—
81C23×Dic11—28no—
82C23×Dic11C23112yes—
83C23×Dic11C23112yes—
84C23×Dic11C23112yes—
85C23×Dic11C2311yescharacteristic
86C23×Dic11C2311yescharacteristic
87C23×Dic11C2311yescharacteristic
88C23×Dic11C2311yescharacteristic
89C23×Dic11C2311yescharacteristic
90C23×Dic11C2311yescharacteristic
91C23×Dic11C2311yescharacteristic
92C23×Dic11C2311yescharacteristic
93C22×Dic22—28no—
94C22×Dic22C23112yes—
95C11×#123C23164yes—
96C2×C11×C4⋊C4C23112yes—
97C2×C11×C4⋊C4C23112yes—
98C2×C11×C22⋊C4C23112yes—
99C2×C11×C22⋊C4C23112yes—
100C2×C11×C22⋊C4C23112yes—
101C2×C22⋊Dic11C23112yes—
102C2×C22⋊Dic11C23112yes—
103C2×C22⋊Dic11C23112yes—
104C2×C22⋊Dic11C23112yes—
105C2×C22⋊Dic11C23112yes—
106#66988C23164yes—
107D4×Dic11C23164yes—
108#66979C23164yescomplemented
109C2×C4⋊Dic11C23112yes—
110C2×C4⋊Dic11C23112yes—
111C2×C4⋊Dic11C23112yes—
112C2×C4⋊Dic11C23112yes—
113C2×Dic11⋊C4C23112yes—
114C2×Dic11⋊C4C23112yes—
115C2×Dic11⋊C4C23112yes—
116C2×Dic11⋊C4C23112yes—
117C2×Dic11⋊C4C23112yes—
118C2×Dic11⋊C4C23112yes—
119C2×Dic11⋊C4C23112yes—
120C2×Dic11⋊C4C23112yes—
121C2×Dic11⋊C4C23112yes—
122C2×Dic11⋊C4C23112yes—
123C2×Dic11⋊C4C23164yescomplemented
124C2×C4×Dic11C23112yes—
125C2×C4×Dic11C23112yes—
126C2×C4×Dic11C23112yes—
127C2×C4×Dic11C23112yes—
128C2×C4×Dic11C23112yes—
129#66943C23164yescomplemented
130#66942C23164yescomplemented
131#66942C23164yescomplemented
132#66940C23164yescomplemented
133#66932C23164yescomplemented
134#66932C23164yescomplemented
135#66931C23164yescomplemented
136#66931C23164yescomplemented
137#66930C23164yescomplemented
138#66930C23164yescomplemented
139C22×#552—111nomaximal, Sylow
140C24×C11—24no—
141C24×C11—24no—
142C24×C11—24no—
143C24×C11—24no—
144C24×C11—24no—
145C24×C11#4118yes—
146C24×C11C2416yes—
147C24×C11C2416yes—
148C24×C11C2411yescharacteristic
149C2×D4×C11—248no—
150C2×D4×C11C24116yes—
151C22×C4×C11—24no—
152C22×C4×C11—248no—
153C22×C4×C11—24no—
154C22×C4×C11—24no—
155C22×C4×C11—24no—
156C22×C4×C11—24no—
157C22×C4×C11C2416yes—
158C22×C4×C11C2416yes—
159C22×C4×C11C2416yes—
160C22×C4×C11C2416yes—
161C22×C4×C11C2416yes—
162C22×C4×C11C24116yes—
163C22×Dic11—248no—
164C22×Dic11—248no—
165C22×Dic11—24no—
166C22×Dic11—248no—
167C22×Dic11—24no—
168C22×Dic11—24no—
169C22×Dic11—24no—
170C22×Dic11—24no—
171C22×Dic11—24no—
172C22×Dic11—24no—
173C22×Dic11#4118yes—
174C22×Dic11C24116yes—
175C22×Dic11C24116yes—
176C22×Dic11C24116yes—
177C22×Dic11C2416yes—
178C22×Dic11C2416yes—
179C22×Dic11C2416yes—
180C22×Dic11C2416yes—
181C22×Dic11C2416yes—
182C22×Dic11C2416yes—
183C22×Dic11C2416yes—
184C22×Dic11C2416yes—
185C2×Dic22—248no—
186C2×Dic22C24116yes—
187C11×C4⋊C4C24116yes—
188C11×C4⋊C4C24116yes—
189C11×C22⋊C4C24116yes—
190C11×C22⋊C4C24116yes—
191C11×C22⋊C4C24116yes—
192C22⋊Dic11C24116yes—
193C22⋊Dic11C24116yes—
194C22⋊Dic11C24116yes—
195C22⋊Dic11C24116yes—
196C22⋊Dic11C24116yes—
197C4⋊Dic11C24116yes—
198C4⋊Dic11C24116yes—
199C4⋊Dic11C24116yes—
200C4⋊Dic11C24116yes—
201Dic11⋊C4C24116yes—
202Dic11⋊C4C24116yes—
203Dic11⋊C4C24116yes—
204Dic11⋊C4C24116yes—
205Dic11⋊C4C24116yes—
206Dic11⋊C4C24116yes—
207Dic11⋊C4C24116yes—
208Dic11⋊C4C24116yes—
209Dic11⋊C4C24116yes—
210Dic11⋊C4C24116yes—
211C4×Dic11C24116yes—
212C4×Dic11C24116yes—
213C4×Dic11C24116yes—
214C4×Dic11C24116yes—
215C4×Dic11C24116yes—
216C2×#552—1148no—
217C22×#126—111no—
218C22×#126—111no—
219C22×#125—111no—
220C22×#125—111no—
221C22×#125—111no—
222C22×#123—111no—
223C22×#123D1111yescharacteristic
224C22×C22⋊Q8—111no—
225C22×C22⋊Q8—111no—
226C22×C4×Q8—111no—
227C22×C4×D4—111no—
228C22×#117—111no—
229C22×#117—111no—
230C22×#117—111no—
231C23×C4⋊C4—111no—
232C23×C11—232no—
233C23×C11—212no—
234C23×C11—212no—
235C23×C11—212no—
236C23×C11—212no—
237C23×C11—212no—
238C23×C11—416no—
239C23×C11C2×#41124yes—
240C23×C11C2×#4114yes—
241C23×C11C2×#4114yes—
242C23×C112−1+414yes—
243C23×C11C2514yes—
244C23×C11C2514yes—
245C23×C11C2513yes—
246D4×C11—232no—
247C2×C4×C11—212no—
248C2×C4×C11—232no—
249C2×C4×C11—212no—
250C2×C4×C11—212no—
251C2×C4×C11—212no—
252C2×C4×C11—212no—
253C2×C4×C11C2514yes—
254C2×C4×C11C2514yes—
255C2×C4×C11C2514yes—
256C2×C4×C11C2514yes—
257C2×C4×C11C2514yes—
258C2×Dic11—212no—
259C2×Dic11—232no—
260C2×Dic11—212no—
261C2×Dic11—212no—
262C2×Dic11—212no—
263C2×Dic11—212no—
264C2×Dic11—212no—
265C2×Dic11—212no—
266C2×Dic11—232no—
267C2×Dic11—232no—
268C2×Dic11C2×#41124yes—
269C2×Dic11C2514yes—
270C2×Dic11C2514yes—
271C2×Dic11C2514yes—
272C2×Dic11C2514yes—
273C2×Dic11C2514yes—
274C2×Dic11C2514yes—
275C2×Dic11C2514yes—
276C2×Dic11C2514yes—
277Dic22—232no—
278C23×Q8—111no—
279C23×D4C2×D1111yescharacteristic
280C24×C4—111no—
281C24×C4—111no—
282C24×C4—111no—
283C24×C4C2×D1111yescharacteristic
284#552—11256no—
285C2×#126—1124no—
286C2×#126—1124no—
287C2×#125—1124no—
288C2×#125—1124no—
289C2×#125—1124no—
290C2×#123—1124no—
291C2×#123C2×D11124yes—
292C2×C22⋊Q8—1124no—
293C2×C22⋊Q8—1124no—
294C2×C4×Q8—1124no—
295C2×C4×D4—1124no—
296C2×#117—1124no—
297C2×#117—1124no—
298C2×#117—1124no—
299C22×C4⋊C4—111no—
300C22×C4⋊C4—111no—
301C22×C4⋊C4—111no—
302C22×C4⋊C4—111no—
303C22×C4⋊C4—111no—
304C22×C4⋊C4—111no—
305C22×C4⋊C4—111no—
306C22×C4⋊C4—111no—
307C22×C4⋊C4—111no—
308C22×C4⋊C4—111no—
309C22×C4⋊C4—1124no—
310C22×C4⋊C4—111no—
311C22×C4⋊C4—111no—
312C22×C4⋊C4—111no—
313C22×C4⋊C4—111no—
314C22×C4⋊C4C2×D1111yescharacteristic
315C22×C4⋊C4C2×D1111yescharacteristic
316C22×C22⋊C4—111no—
317C22×C22⋊C4—111no—
318C22×C22⋊C4—111no—
319C22×C22⋊C4—111no—
320C22×C22⋊C4—111no—
321C22×C22⋊C4C2×D1111yescharacteristic
322C22×C22⋊C4C2×D1111yescharacteristic
323C22×C22⋊C4C2×D1111yescharacteristic
324C22×C42—111no—
325C22×C42—111no—
326C22×C42—111no—
327C22×C42—111no—
328C22×C42—111no—
329C22×C11—24no—
330C22×C11—24no—
331C22×C11—248no—
332C22×C11—24no—
333C22×C11—24no—
334C22×C11—24no—
335C22×C11—424no—
336C22×C11#552116yescomplemented
337C22×C11C22×#4118yes—
338C22×C11C22×#4116yes—
339C22×C11C22×#4116yes—
340C22×C11C2×2−1+416yes—
341C22×C11C2611yescharacteristic
342C4×C11—24no—
343C4×C11—24no—
344C4×C11—24no—
345C4×C11—24no—
346C4×C11—24no—
347Dic11—24no—
348Dic11—24no—
349Dic11—24no—
350Dic11—24no—
351Dic11—24no—
352Dic11—24no—
353Dic11—24no—
354Dic11C22×#4118yes—
355C25C22×D1111yescharacteristic
356C25C22×D1111yescharacteristic
357C22×Q8—1112no—
358C22×Q8—228no—
359C22×D4—28no—
360C22×D4C22×D11112yes—
361C23×C4—28no—
362C23×C4—111no—
363C23×C4—1112no—
364C23×C4—1112no—
365C23×C4—1112no—
366C23×C4—111no—
367C23×C4—111no—
368C23×C4—111no—
369C23×C4—111no—
370C23×C4—111no—
371C23×C4—111no—
372C23×C4—111no—
373C23×C4—228no—
374C23×C4—228no—
375C23×C4—228no—
376C23×C4C22×D11112yes—
377C23×C4C22×D1111yescharacteristic
378C23×C4C22×D1111yescharacteristic
379C23×C4C22×D1111yescharacteristic
380C23×C4C22×D1111yescharacteristic
381C23×C4C22×D1111yescharacteristic
382#126—1164no—
383#126—1164no—
384#125—1164no—
385#125—1164no—
386#125—1164no—
387#123—1164no—
388#123C22×D11164yes—
389C22⋊Q8—1164no—
390C22⋊Q8—1164no—
391C4×Q8—1164no—
392C4×D4—1164no—
393#117—1164no—
394#117—1164no—
395#117—1164no—
396C2×C4⋊C4—1112no—
397C2×C4⋊C4—1112no—
398C2×C4⋊C4—1112no—
399C2×C4⋊C4—1112no—
400C2×C4⋊C4—1164no—
401C2×C4⋊C4—1112no—
402C2×C4⋊C4—1112no—
403C2×C4⋊C4—1112no—
404C2×C4⋊C4—1112no—
405C2×C4⋊C4—1112no—
406C2×C4⋊C4—1112no—
407C2×C4⋊C4—1112no—
408C2×C4⋊C4—1112no—
409C2×C4⋊C4—1112no—
410C2×C4⋊C4—1112no—
411C2×C4⋊C4C22×D11112yes—
412C2×C4⋊C4C22×D11112yes—
413C2×C22⋊C4—1112no—
414C2×C22⋊C4—1112no—
415C2×C22⋊C4—1112no—
416C2×C22⋊C4—1112no—
417C2×C22⋊C4—1112no—
418C2×C22⋊C4C22×D11112yes—
419C2×C22⋊C4C22×D11112yes—
420C2×C22⋊C4C22×D11112yes—
421C2×C42—1112no—
422C2×C42—1112no—
423C2×C42—1112no—
424C2×C42—1112no—
425C2×C42—1112no—
426C2×C11—28no—
427C2×C11—44no—
428C2×C11C2×#552112yescomplemented
429C2×C11C23×#4111yescharacteristic
430C2×C11C23×#4111yescharacteristic
431C2×C11C22×2−1+411yescharacteristic
432C24—24no—
433C24—24no—
434C24—24no—
435C24—24no—
436C24—24no—
437C24#434118yes—
438C24C23×D1116yes—
439C24C23×D1116yes—
440C24C23×D1111yescharacteristic
441C2×Q8—1116no—
442C2×Q8—2248no—
443C2×D4—248no—
444C2×D4C23×D11116yes—
445C22×C4—248no—
446C22×C4—24no—
447C22×C4—24no—
448C22×C4—24no—
449C22×C4—24no—
450C22×C4—24no—
451C22×C4—118no—
452C22×C4—116no—
453C22×C4—116no—
454C22×C4—116no—
455C22×C4—116no—
456C22×C4—116no—
457C22×C4—116no—
458C22×C4—116no—
459C22×C4—116no—
460C22×C4—1116no—
461C22×C4—1116no—
462C22×C4—1116no—
463C22×C4—2248no—
464C22×C4—2248no—
465C22×C4—2248no—
466C22×C4—224no—
467C22×C4—224no—
468C22×C4—224no—
469C22×C4—224no—
470C22×C4—224no—
471C22×C4—224no—
472C22×C4—224no—
473C22×C4C23×D1116yes—
474C22×C4C23×D1116yes—
475C22×C4C23×D1116yes—
476C22×C4C23×D1116yes—
477C22×C4C23×D1116yes—
478C22×C4C23×D11116yes—
479C4⋊C4—1116no—
480C4⋊C4—1116no—
481C4⋊C4—1116no—
482C4⋊C4—1116no—
483C4⋊C4—1116no—
484C4⋊C4—1116no—
485C4⋊C4—1116no—
486C4⋊C4—1116no—
487C4⋊C4—1116no—
488C4⋊C4—1116no—
489C4⋊C4—1116no—
490C4⋊C4—1116no—
491C4⋊C4—1116no—
492C4⋊C4—1116no—
493C4⋊C4C23×D11116yes—
494C4⋊C4C23×D11116yes—
495C22⋊C4—1116no—
496C22⋊C4—1116no—
497C22⋊C4—1116no—
498C22⋊C4—1116no—
499C22⋊C4—1116no—
500C22⋊C4C23×D11116yes—
501C22⋊C4C23×D11116yes—
502C22⋊C4C23×D11116yes—
503C42—1116no—
504C42—1116no—
505C42—1116no—
506C42—1116no—
507C42—1116no—
508C11C22×#55211yescharacteristic, complemented, Sylow
509C23—232no—
510C23—212no—
511C23—212no—
512C23—212no—
513C23—212no—
514C23—212no—
515C23—416no—
516C23C2×#4341124yes—
517C23C2×#434114yes—
518C23#41×D1114yes—
519C23#6704314yes—
520C23C24×D1114yes—
521C23C24×D1114yes—
522C23C24×D1113yes—
523Q8—2232no—
524D4—232no—
525C2×C4—232no—
526C2×C4—212no—
527C2×C4—212no—
528C2×C4—212no—
529C2×C4—212no—
530C2×C4—212no—
531C2×C4—1124no—
532C2×C4—114no—
533C2×C4—114no—
534C2×C4—114no—
535C2×C4—114no—
536C2×C4—114no—
537C2×C4—114no—
538C2×C4—114no—
539C2×C4—114no—
540C2×C4—2232no—
541C2×C4—2232no—
542C2×C4—2232no—
543C2×C4—2212no—
544C2×C4—2212no—
545C2×C4—2212no—
546C2×C4—2212no—
547C2×C4—2212no—
548C2×C4—2212no—
549C2×C4—2212no—
550C2×C4C24×D1114yes—
551C2×C4C24×D1114yes—
552C2×C4C24×D1114yes—
553C2×C4C24×D1114yes—
554C2×C4C24×D1114yes—
555C22—248no—
556C22—24no—
557C22—24no—
558C22—24no—
559C22—24no—
560C22—24no—
561C22—424no—
562C22#10623181116yesdirect product factor
563C22C22×#434118yes—
564C22C22×#434116yes—
565C22C2×#41×D1116yes—
566C22C2×#6704316yes—
567C22C25×D1111yescharacteristic
568C4—24no—
569C4—24no—
570C4—24no—
571C4—24no—
572C4—24no—
573C4—118no—
574C4—224no—
575C4—224no—
576C4—224no—
577C4—224no—
578C4—224no—
579C4—224no—
580C4—224no—
581C2—28no—
582C2—44no—
583C2C2×#10623181112yesdirect product factor
584C2C22×#41×D1111yescharacteristic
585C2C23×#434111yescharacteristic
586C2C22×#6704311yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC22×C11×#123C2
socleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC22×#123D11
hypocenterC11C22×#552
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#123

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#10623181C2direct (N × H)
2. C22×#66932C2semidirect
3. C22×#66932C2semidirect
4. C22×#66943C2semidirect
5. C22×#66942C2semidirect
6. C22×#66942C2semidirect
8. C22×#66931C2semidirect
9. C22×#66931C2semidirect
10. C22×#66940C2semidirect
12. C22×#66979C2semidirect
13. C22×#66930C2semidirect
14. C22×#66930C2semidirect
15. C23×Dic11⋊C4C2semidirect
36. C2×#66979C22semidirect
51. C22×Dic11⋊C4C22semidirect
57. #10623181C22direct (N × H)
58. C2×#66943C22semidirect
59. C2×#66942C22semidirect
60. C2×#66942C22semidirect
61. C2×#66940C22semidirect
62. C2×#66932C22semidirect
63. C2×#66932C22semidirect
64. C2×#66931C22semidirect
65. C2×#66931C22semidirect
66. C2×#66930C22semidirect
67. C2×#66930C22semidirect
108. #66979C23semidirect
123. C2×Dic11⋊C4C23semidirect
129. #66943C23semidirect
130. #66942C23semidirect
131. #66942C23semidirect
132. #66940C23semidirect
133. #66932C23semidirect
134. #66932C23semidirect
135. #66931C23semidirect
136. #66931C23semidirect
137. #66930C23semidirect
138. #66930C23semidirect
336. C22×C11#552semidirect
428. C2×C11C2×#552semidirect
508. C11C22×#552semidirect
562. C22#10623181direct (N × H)
583. C2C2×#10623181direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#106231812
C22×#669322
C22×#669432
C22×#669422
C22×#669882
C22×#669312
C22×#669402
C22×D4×Dic112
C22×#669792
C22×#669302
C23×Dic11⋊C42
C22×C11×#1232
C22×#55211